1. Field of the Invention
The present invention relates to an inductor used for radio communications in microwave and millimeter wave bands or transmission and reception of electromagnetic waves, and to a filter including the inductor.
2. Description of the Related Art
Inductors having an air-bridge structure are disclosed in Japanese Patent No. 3450713 and Japanese Unexamined Patent Application Publication No. 2007-67236. Such an inductor has an electrode that is partially floating from a substrate thereof.
The inductor disclosed in Japanese Patent No. 3450713 has an air-bridge structure in which a conductor pattern having a chevron cross-sectional shape floats from a substrate in order to increase the cross-sectional area of the conductor pattern.
The inductor disclosed in Japanese Unexamined Patent Application Publication No. 2007-67236 has an air-bridge structure in which a first layer conductor pattern and a second layer conductor pattern laminated on a substrate are serially connected.
Although these inductors ideally have only an inductance component, the actual circuit thereof has a resistance component and causes a resistance loss. As the inductor gets closer to a pure inductance, the Q value of the inductor increases. A large Q value inductor is preferable. The Q value of the inductor is expressed by the following equation:Q=ωL/r where ω represents an operating frequency (angular frequency), L represents an inductance component L, and r represents a resistance component.
In high-frequency bands, such as microwave and millimeter wave bands, current distribution (skin effect) is pronounced within a conductor, and the skin effect of an electrode increases the resistance component. For example, if a gold electrode is used in the 2 GHz band, the skin depth is δs=about 1.7 μm, which is less than a thickness of an electrode made of typical plate (for example, about 6 μm or greater). Current is concentrated in an electrode subsurface portion to as thick as about 1.7 μm, thereby increasing the resistance component r of the inductor.
The inductor disclosed in Japanese Patent No. 3450713 has a conductor with an increased cross-sectional area. Because of the skin effect, an increase in the cross-sectional area of the conductor does not significantly contribute to controlling an increase in the resistance component r. Accordingly, the Q value of the inductor cannot be sufficiently increased as would be expected.
In accordance with Japanese Unexamined Patent Application Publication No. 2007-67236, the serial connection of the first layer conductor pattern and the second layer conductor pattern increases a total inductance value L, thereby increasing the Q value of the inductor. However, with this arrangement, a large air gap is required to control parasitic capacity. A coil at a top tier must be mounted at a high level position above the substrate as compared to the thickness of an electrode. Thus, miniaturization (low-profile design) is difficult to achieve. Furthermore, the coil at the top tier is permitted to be connected to a coil at a lower tier at only one point, and the structural strength of the inductor cannot be maintained at a sufficient level.